If you're a city dweller who relies on subways, buses, and cabs, you'll need a lightweight but sturdy stroller that folds quickly and is compact. A car seat carrier frame would work well, or a light, basic travel system. For your older infant (over 6 months) or toddler, consider a lightweight umbrella stroller. A sturdier stroller, perhaps one with larger tires, may be easier to push if you'll be going for long walks. But a bigger, heavier stroller might be harder to lift and fit into your car trunk, or to use on public transportation.
Some traditional and all-terrain strollers may have better shock-absorption, a three wheel configuration, and a seat that gives your baby more support than a simple umbrella stroller. This is also true of jogging strollers, but there's no reason to buy a jogger unless you're going to run with it. If you'll be tromping through snow or on unpaved roads or grass, a model with large wheels is a great option. Under those same conditions, a stroller with small plastic wheels might be difficult to push. If you want to run, use a jogging stroller only, with a fixed front wheel, or locked swivel wheel.
If you do have a car, make sure whatever stroller you choose fits inside easily. And give some thought to where you will put a folded, standing stroller in your house. Do you have the closet space for it? Or will it block a hallway if you have to store it there? A folded stroller in the hall, or standing inside a closet, might also be a tip-over hazard for a curious baby or toddler.
Some parents may start with a travel system and later add a lightweight umbrella stroller for quick trips when baby is a bit older. If one parent will be on his or her own with the kids, consider getting something that's not too heavy since you may also be carrying a diaper bag and a child. A stroller you can open and close with one hand also helps, but many strollers don't have this feature. A deep storage basket makes a big difference when you're out running errands. Owning a stroller that comes with a car seat (such as a travel system) or is compatible with an infant car seat you own can also simplify your life.
For two children, you can buy a tandem or a side-by-side stroller. Depending on the model and configuration, some of these can be used with children of different ages. Some double strollers are of the sit-and-stand variety, where one seat is either car-seat compatible or infant ready, while the second is for your older child. Many of these also have a platform for the older child to ride (with a safety belt to make sure he doesn't fall off).